Modified Spiegler-Kedem Model to Predict the Rejection and Flux of Nanofiltration Processes at High NaCl Concentrations

Abstract

Current nanofiltration (NF) models are based on the “diluted solution” assumption and cannot successfully predict permeate fluxes at high salt concentrations. The reasons behind the strong differences between the predicted and observed fluxes are still not fully understood. In this work, it is proposed that these deviations are possibly caused by the electrical charges inside the membrane pores. At a nanoscale level, the complex electrostatic interactions between the highly confined charged solutes and the charges inside membrane pores contribute to flow retardation and this phenomena can be characterized using an additional resistance factor, which is defined as the electric resistance factor in this study. To this extent, experiments were carried out with aqueous sodium chloride (NaCl) solutions in a wide range of concentrations (0.05 – 1.96 M) using two commercial membranes (NF270 and Desal-5 DL). Salt retention was fitted and analysed by means of the classical Spiegler-Kedem model (SK). The model has been modified to include the proposed empirical electric resistance factor, Relec, to account for this additional hydrodynamic flow resistance. The modified Spiegler-Kedem model (MSK) was verified by fitting experimental data at relatively low salt concentration to obtain model parameters and then comparing the model prediction with experimental data at higher concentrations. A mathematical equation was developed to describe the dependence of an important model parameter, reflection coefficient (σ), on operational conditions such as pressure and bulk salt concentration. The thesis also discussed the mechanisms of NF separation, highlighting the electrostatic interaction between the co-ions and the membrane charges in the confined nano-environment inside the NF membrane pores.